I Description of Adiabatic Expansion

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I've seen the derivation for the adiabatic expansion of an ideal gas which gives the result ## TV^{\gamma - 1} = constant ## which I understand. I have also seen the a similar result, ## pV^{\gamma} = constant ##. But I can't see how to get from the first expression to the second. Any ideas?
 

hilbert2

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If you put ##\frac{PV}{nR}## in place of ##T## in the first equation, doesn't it become the second one, assuming that the number of moles ##n## remains constant in the expansion?
 
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From doing that you get ## pV^{\gamma} = R(constant) ##. So you just define a new constant on the RHS that contains ## R ##?
 

sophiecentaur

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Isn't this a straightforward bit of Text Book derivation? Do you not have access to one?
 

hilbert2

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Yes, it's a different constant then, the original one multiplied by ##nR##.
 

sophiecentaur

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If you don't have a text book, try the Hyperphysics website. They have a fair amount of stuff on the gas laws.
 
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Isn't this a straightforward bit of Text Book derivation? Do you not have access to one?
You are probably right, however I don't have a textbook on thermodynamics. I thought of substituting ## \frac{pV}{nR} ## but didn't see how to remove ## nR ## from the final expression. Since they're constant, I guess it's obvious the new constant contains these terms.
 
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sophiecentaur

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Thanks, I'll check it out :thumbup:.
There are other on-line sources which are an alternative to a text book but Hyperphysics is fairly user friendly.
 

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